LCM of 420, 819, 108, 312
Reviewed By : Rajashekhar Valipishetty
Last Updated at : Mar 29,2023
Find the LCM of 420, 819, 108, 312 with the LCM of Two or More Numbers Calculator. Here we are teaching you two different methods through which you can calculate the LCM of 420, 819, 108, 312. So, keep reading to learn more.
Given numbers are 420,819,108,312
The least common multiple of numbers can be find using the prime factorization method or LCM formula.
The LCM of 420,819,108,312 is 98280.
Find LCM of 420,819,108,312 with Prime Factorization
| 2 | 420, 819, 108, 312 |
| 2 | 210, 819, 54, 156 |
| 3 | 105, 819, 27, 78 |
| 3 | 35, 273, 9, 26 |
| 7 | 35, 91, 3, 26 |
| 13 | 5, 13, 3, 26 |
| 5, 1, 3, 2 |
Multiply the prime numbers at the bottom and the left side.
2 x 2 x 3 x 3 x 7 x 13 x 5 x 1 x 3 x 2 = 98280
Therefore, the lowest common multiple of 420,819,108,312 is 98280.
LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
Firstly, we have to find the product of all the numbers.
420 x 819 x 108 x 312 = 11590750080
Then, let us find the GCF of these five numbers. To do so, we have to list down the factors for each number and choose the highest factor that is in all of the lists.
420 : 1, 2, 3, 4, 5, 6, 7, 10, 12, 14, 15, 20, 21, 28, 30, 35, 42, 60, 70, 84, 105, 140, 210, 420
819 : 1, 3, 7, 9, 13, 21, 39, 63, 91, 117, 273, 819
108 : 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 108
312 : 1, 2, 3, 4, 6, 8, 12, 13, 24, 26, 39, 52, 78, 104, 156, 312
3 is the greatest number that appears in all the lists. Therefore, we can determine that the GCF of 420,819,108,312, is 3.
Now, the common factors can be found like this.
420:2x 2x 3x 5x 7
819:3x 3x 7x 13
108:2x 2x 3x 3x 3
312:2x 2x 2x 3x 13
From this, we can see that the common factors because they appear for more than two numbers. So, just multiply them all together.
2x 2x 2x 2x 3x 3x 3x 7x 13 = 39312
Therefore, the value for common factors is 39312.
Now that we have all the elements of the formula, we can plug them in to calculate the LCM.
LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}
LCM = 11590750080/(3x39312)
LCM = 11590750080/117936
LCM = 98280
Thus, we can understand that the LCM of 420,819,108,312 is 98280.
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FAQs on LCM of 420, 819, 108, 312
1. What is the LCM of 420, 819, 108, 312?
Answer: LCM of 420, 819, 108, 312 is 98280.
2. How to calculate the LCM of 420, 819, 108, 312?
The LCM can be found using two methods. You can either use the LCM formula or the prime factorization method to calculate the LCM of 420, 819, 108, 312.
3. What is the LCM formula?
The LCM formula is LCM(a1, a2, an) = (a1 x a2 x an)/{GCF(a1 x a2 x an) x common factors}.